Solving proportions with cross multiplication
If a/b = c/d, multiplying both sides by b and by d gives a × d = b × c. That single rule, often called cross multiplication, is all you need to find any one missing value. The calculator writes out each line so you can copy the working into homework or check your own answer.
Worked examples
Recipe scaling. A recipe uses 3 eggs for 4 servings. How many eggs for 10 servings? 3/4 = x/10, so 4x = 30 and x = 7.5. Round to 7 or 8 depending on egg size.
Map scale. On a map 2 cm represents 5 km. Two towns are 13 cm apart: 2/5 = 13/x, so 2x = 65 and x = 32.5 km.
Unit price. If 12 oz of coffee costs $9.60, what do 32 oz cost? 12/9.60 = 32/x, so 12x = 307.2 and x = $25.60.
Is it a proportion?
Two ratios are proportional only when their cross products match. That makes the test quick: 4/10 and 6/15 give 60 and 60, so they are proportional; 4/10 and 5/12 give 48 and 50, so they are not. Turn on the checker in the calculator and it compares the cross products for you.
Where proportions show up
- Converting units and currencies at a fixed rate.
- Similar triangles and scale drawings in geometry.
- Dosage-style problems in science classes, concentration and dilution.
- Estimating materials: if 3 bags cover 40 sq ft, how many cover 250? Our square footage calculator helps find the area first.
For ratios with more than two terms, or to simplify a ratio to lowest terms, switch to the ratio calculator.
Frequently asked questions
What is a proportion?
A proportion is an equation stating that two ratios are equal, such as 3/4 = 15/20. Both sides describe the same relationship at a different scale.
How do you solve a proportion?
Cross-multiply: multiply the numerator of each fraction by the denominator of the other, set the products equal, and divide to isolate the unknown. For 3/4 = x/20, 4x = 60 so x = 15.
How can I tell if two ratios are proportional?
They are proportional when their cross products are equal. 6/8 and 9/12 are proportional because 6 × 12 = 72 and 8 × 9 = 72.
What is the difference between direct and inverse proportion?
In a direct proportion both quantities grow together (twice the gas, twice the distance). In an inverse proportion one grows as the other shrinks (twice the workers, half the time). This calculator solves direct proportions.
Can I use decimals or negative numbers?
Yes. Any real numbers work, as long as the value you divide by in the final step is not zero.
Sources and official references
- Proportional relationships (Grade 7 math) – Khan Academy
Last reviewed October 10, 2026. Results are estimates for planning; see our disclaimer.
